Q: What are the factor combinations of the number 120,475?

 A:
Positive:   1 x 1204755 x 2409525 x 481961 x 197579 x 1525305 x 395
Negative: -1 x -120475-5 x -24095-25 x -4819-61 x -1975-79 x -1525-305 x -395


How do I find the factor combinations of the number 120,475?

Unfortunately, there's not simple formula to identifying all of the factors of a number and it can be a tedious process when trying to identify the divisors of larger numbers. To find the factor combinations of the number 120,475, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

We start by creating a table and writing 1 on the left side and then the number we're trying to find the factors for on the right side in a table. Then, below that, write the numbers as a negative as well.

1 120,475
-1 -120,475

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 120,475.

Example:
1 x 120,475 = 120,475
and
-1 x -120,475 = 120,475
Notice both answers equal 120,475

With that explanation out of the way, let's continue. Next, we take the number 120,475 and divide it by 2:

120,475 ÷ 2 = 60,237.5

If the quotient is a whole number, then 2 and 60,237.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 120,475
-1 -120,475

Now, we try dividing 120,475 by 3:

120,475 ÷ 3 = 40,158.3333

If the quotient is a whole number, then 3 and 40,158.3333 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 120,475
-1 -120,475

Let's try dividing by 4:

120,475 ÷ 4 = 30,118.75

If the quotient is a whole number, then 4 and 30,118.75 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 120,475
-1 120,475
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

152561793053951,5251,9754,81924,095120,475
-1-5-25-61-79-305-395-1,525-1,975-4,819-24,095-120,475

More Examples

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